Sudoku method
How can I use a 4x4 Sudoku to construct a 4x4 (pan)magic square?
Most times a Sudoku consists of 9 rows and 9 columns. In each row and in each column (and in each 3x3 sub-square) you find all the numbers from 1 up to 9. Use a 4x4 Sudoku to construct a 4x4 (pan)magic square in only 4 steps:
(1st) Fill in the 4x4 Sudoku with the numbers 0, 1, 2, 3. Take care that all the numbers from 0 up to 3 are in each row, column and diagonal.
(2nd) Construct the second 4x4 Sudoku by rotating the first Sudoku by a quarter to the right.
(3rd) Take 4x number from the first Sudoku and add 1x number from the same cell of the second Sudoku.
(4th) Finally add 1 to each cell.
4x number + 1x number = +1 = magic square
|
0 |
1 |
2 |
3 |
2 |
1 |
3 |
0 |
2 |
5 |
11 |
12 |
3 |
6 |
12 |
13 |
|||
|
3 |
2 |
1 |
0 |
3 |
0 |
2 |
1 |
15 |
8 |
6 |
1 |
16 |
9 |
7 |
2 |
|||
|
1 |
0 |
3 |
2 |
0 |
3 |
1 |
2 |
4 |
3 |
13 |
10 |
5 |
4 |
14 |
11 |
|||
|
2 |
3 |
0 |
1 |
1 |
2 |
0 |
3 |
9 |
14 |
0 |
7 |
10 |
15 |
1 |
8 |
This magic square happens to be panmagic!
Use this method [Sudoku method (1)] to construct magic squares of order is 2^n (= 2x2, 2x2x2, 2x2x2x2, ...) from 4x4 to infinity. See 4x4, 8x8, 16x16, 32x32
